Write in Standard Form f(x)=(x-2)(x-3)(x-5)

$f (x) = (x - 2) (x - 3) (x - 5)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$f (x) = a x^{2} + b x + c$

Step 2

Expand $(x - 2) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$f (x) = (x (x - 3) - 2 (x - 3)) (x - 5)$

Apply the distributive property.

$f (x) = (x \cdot x + x \cdot - 3 - 2 (x - 3)) (x - 5)$

Apply the distributive property.

$f (x) = (x \cdot x + x \cdot - 3 - 2 x - 2 \cdot - 3) (x - 5)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$f (x) = (x^{2} + x \cdot - 3 - 2 x - 2 \cdot - 3) (x - 5)$

Move $- 3$ to the left of $x$ .

$f (x) = (x^{2} - 3 \cdot x - 2 x - 2 \cdot - 3) (x - 5)$

Multiply $- 2$ by $- 3$ .

$f (x) = (x^{2} - 3 x - 2 x + 6) (x - 5)$

Subtract $2 x$ from $- 3 x$ .

$f (x) = (x^{2} - 5 x + 6) (x - 5)$

Step 4

Expand $(x^{2} - 5 x + 6) (x - 5)$ by multiplying each term in the first expression by each term in the second expression.

$f (x) = x^{2} x + x^{2} \cdot - 5 - 5 x \cdot x - 5 x \cdot - 5 + 6 x + 6 \cdot - 5$

Step 5

Simplify terms.

Simplify each term.

Multiply $x^{2}$ by $x$ by adding the exponents.

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$f (x) = x^{2} x + x^{2} \cdot - 5 - 5 x \cdot x - 5 x \cdot - 5 + 6 x + 6 \cdot - 5$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (x) = x^{2 + 1} + x^{2} \cdot - 5 - 5 x \cdot x - 5 x \cdot - 5 + 6 x + 6 \cdot - 5$

Add $2$ and $1$ .

$f (x) = x^{3} + x^{2} \cdot - 5 - 5 x \cdot x - 5 x \cdot - 5 + 6 x + 6 \cdot - 5$

Move $- 5$ to the left of $x^{2}$ .

$f (x) = x^{3} - 5 \cdot x^{2} - 5 x \cdot x - 5 x \cdot - 5 + 6 x + 6 \cdot - 5$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$f (x) = x^{3} - 5 x^{2} - 5 (x \cdot x) - 5 x \cdot - 5 + 6 x + 6 \cdot - 5$

Multiply $x$ by $x$ .

$f (x) = x^{3} - 5 x^{2} - 5 x^{2} - 5 x \cdot - 5 + 6 x + 6 \cdot - 5$

Multiply $- 5$ by $- 5$ .

$f (x) = x^{3} - 5 x^{2} - 5 x^{2} + 25 x + 6 x + 6 \cdot - 5$

Multiply $6$ by $- 5$ .

$f (x) = x^{3} - 5 x^{2} - 5 x^{2} + 25 x + 6 x - 30$

Simplify by adding terms.

Subtract $5 x^{2}$ from $- 5 x^{2}$ .

$f (x) = x^{3} - 10 x^{2} + 25 x + 6 x - 30$

Add $25 x$ and $6 x$ .

$f (x) = x^{3} - 10 x^{2} + 31 x - 30$

Write in Standard Form f(x)=(x-2)(x-3)(x-5)

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